https://peda.net/id/e85cf914ed6 2018-11-21T10:24:47+02:00 https://peda.net/:static/532/peda.net.logo.bg.svg <div class="license">Tämän sivun lisenssi <a rel="license" href="https://peda.net/info">Peda.net-yleislisenssi</a></div> https://peda.net/id/31de5e08f3c 2018-11-29T12:47:41+02:00 <div><img src="https://math-demo.abitti.fi/math.svg?latex=D%5Ctan%20x%3D%5Cfrac%7B1%7D%7B%5Ccos%5E2x%7D%3D1%2B%5Ctan%5E2x" alt="D\tan x=\frac{1}{\cos^2x}=1+\tan^2x"/></div> <img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(x%5Cright)%3D2%5Ctan%20x-3%5Ccos%20x" alt="f\left(x\right)=2\tan x-3\cos x"/> <div>Funktion ja y-akselin leikkauspistessa x=0</div> <div>Lasketaan leikkauspisteen y-koordinaatti</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=f%5Cleft(0%5Cright)%3D2%5Ctan0-3%5Ccos0%3D2%5Ccdot0-3%5Ccdot1%3D-3" alt="f\left(0\right)=2\tan0-3\cos0=2\cdot0-3\cdot1=-3"/></div> <div>Leikkauspiste on (0,-3)</div> <div>Tangentin kulmakerroin on dervaatan arvo kohdassa x=0</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=f%27%5Cleft(x%5Cright)%3D%5Cfrac%7B2%7D%7B%5Ccos%5E2x%7D%2B3%5Csin%20x" alt="f'\left(x\right)=\frac{2}{\cos^2x}+3\sin x"/></div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=f%27%5Cleft(0%5Cright)%3D%5Cfrac%7B2%7D%7B%5Cleft(%5Ccos0%5Cright)%5E2%7D%2B3%5Csin0%3D2" alt="f'\left(0\right)=\frac{2}{\left(\cos0\right)^2}+3\sin0=2"/></div> <div>tai</div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=f%27%5Cleft(x%5Cright)%3D2%5Cleft(1%2B%5Ctan%5E2x%5Cright)%2B3%5Csin%20x%3D2%2B2%5Ctan%5E2x%2B3%5Csin%20x" alt="f'\left(x\right)=2\left(1+\tan^2x\right)+3\sin x=2+2\tan^2x+3\sin x"/></div> <img src="https://math-demo.abitti.fi/math.svg?latex=f%27%5Cleft(0%5Cright)%3D2%2B2%5Cleft(%5Ctan0%5Cright)%5E2%2B3%5Csin0%3D2" alt="f'\left(0\right)=2+2\left(\tan0\right)^2+3\sin0=2"/><br/> <div> </div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=y%2B3%3D2%5Cleft(x-0%5Cright)" alt="y+3=2\left(x-0\right)"/></div> <img src="https://math-demo.abitti.fi/math.svg?latex=y%3D2x-3" alt="y=2x-3"/> 2018-11-29T12:47:41+02:00 https://peda.net/id/35049feeed6 2018-11-21T10:48:24+02:00 <div>Ratkaise yhtälö sinx=cos3x hyödytäen kaavaa <img src="https://math-demo.abitti.fi/math.svg?latex=%5Csin%20x%3D%5Ccos%5Cleft(%5Cfrac%7B%5Cpi%7D%7B2%7D-x%5Cright)" alt="\sin x=\cos\left(\frac{\pi}{2}-x\right)"/></div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=%5Csin%20x%3D%5Ccos3x" alt="\sin x=\cos3x"/></div> <br/> <img src="https://math-demo.abitti.fi/math.svg?latex=%5Ccos%5Cleft(%5Cfrac%7B%5Cpi%7D%7B2%7D-x%5Cright)%3D%5Ccos3x" alt="\cos\left(\frac{\pi}{2}-x\right)=\cos3x"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=3x%3D%5Cfrac%7B%5Cpi%7D%7B2%7D-x%2Bn%5Ccdot2%5Cpi%5C%20%5C%20tai%5C%20%5C%203x%3D-%5Cleft(%5Cfrac%7B%5Cpi%7D%7B2%7D-x%5Cright)%2Bn%5Ccdot2%5Cpi" alt="3x=\frac{\pi}{2}-x+n\cdot2\pi\ \ tai\ \ 3x=-\left(\frac{\pi}{2}-x\right)+n\cdot2\pi"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=4x%3D%5Cfrac%7B%5Cpi%7D%7B2%7D%2Bn%5Ccdot2%5Cpi%5C%20%5C%20%5C%20%5C%20" alt="4x=\frac{\pi}{2}+n\cdot2\pi\ \ \ \ "/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D%5Cfrac%7B%5Cpi%7D%7B8%7D%2Bn%5Ccdot%5Cfrac%7B%5Cpi%7D%7B2%7D" alt="x=\frac{\pi}{8}+n\cdot\frac{\pi}{2}"/><br/> <div> </div> <div><img src="https://math-demo.abitti.fi/math.svg?latex=3x%3D-%5Cleft(%5Cfrac%7B%5Cpi%7D%7B2%7D-x%5Cright)%2Bn%5Ccdot2%5Cpi" alt="3x=-\left(\frac{\pi}{2}-x\right)+n\cdot2\pi"/></div> <img src="https://math-demo.abitti.fi/math.svg?latex=3x%3D-%5Cfrac%7B%5Cpi%7D%7B2%7D%2Bx%2Bn%5Ccdot2%5Cpi" alt="3x=-\frac{\pi}{2}+x+n\cdot2\pi"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=2x%3D-%5Cfrac%7B%5Cpi%7D%7B2%7D%2Bn%5Ccdot2%5Cpi" alt="2x=-\frac{\pi}{2}+n\cdot2\pi"/><br/> <img src="https://math-demo.abitti.fi/math.svg?latex=x%3D-%5Cfrac%7B%5Cpi%7D%7B4%7D%2Bn%5Ccdot%5Cpi" alt="x=-\frac{\pi}{4}+n\cdot\pi"/> 2018-11-21T10:48:24+02:00